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computational with intersecting circles, tangents from a point of one circle

Source: Sharygin 2005 finals 10.5

August 29, 2019
geomatrydistancecirclesTangentsgeometry

Problem Statement

Two circles of radius 11 intersect at points X,YX, Y, the distance between which is also equal to 11. From point CC of one circle, tangents CA,CBCA, CB are drawn to the other. Line CBCB will cross the first circle a second time at point A′A'. Find the distance AA′AA'.
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